Yes there is - I got that stamp and it immediately said that a mini-game was available (I think it was from the port early on - the one where you can train on the beach again if you want to). Mind you, I got that playing one-player, and as the mini-game it unlocked was multiplayer only I haven't had chance to get everybody together to try it out again yet!
For everybody worried about the singleplayer side of things, I don;t actually think it's that bad. Multiplayer is certainly where the game wants to be, but it's not terrible or anything alone.
Oh, and yes you can play in single then add people in to your existing adventure as they visit etc. You don't always need to have everybody/anybody(!) there to continue your game.